So you want to play/draft Magic Online without MODO. That's cool. You'll need two things.
The first thing you need is Magic Workstation. This lets you play the game and construct decks and stuff. Dowload the evaluation version (the group behind this program is now defunct) and install it (it may recommend you to install in C:\MWS instead of C:\Program Files, this is a Windows 7 thingy like with League of Legends).
Now get the MasterBase that contains all the cards up to Return to Ravnica (latest version 9.20.12). Put this file into your MWS install directory (replace the one that's there). NB: There is currently a bug with this MasterBase file that will crash the program if you go into so-called "deck edit mode". For now, just don't do it (stay in "classic view").
Second, you need to get NetDraft. This is the drafting client (obv). Unzip it and throw the folder anywhere. NB: The current NetDraft patch has a few errors, the most important being Risen Sanctuary (8/8 Vigilance) at common (it should be uncommon) and Sundering Growth at 1CC (should cost 2 hybrid mana).
Now you're done! Join #draft4you on irc.solidirc.com to look for drafts (or ones we privately host). Open up NetDraft and enter the IP. When the draft starts, double-click to draft, right-click to show the card. Then make your deck, save it (I recommend saving into your MWS install directory), open it with MWS and play vs your opponent. I may write a more detailed tutorial for how to actually use these programs later, but for now this is a serviceable tutorial.
mwBase patch date: Setp 26, 2012
NetDraft patch date: Setp 20, 2012